Finite Group Databasebeta

← #15685172

Subgroups — #15685172

Order 2944.

448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093230C212yesmaximal, complemented
2#13093223C212yesmaximal, complemented
3#13092689C212yesmaximal, complemented
4#13092677C212yesmaximal, complemented
5#13092599C212yesmaximal, complemented
6#13092594C211yesmaximal, characteristic, complemented
7#13092589C211yesmaximal, characteristic, complemented
8#13092540C212yesmaximal, complemented
9C23×#497C211yesmaximal, characteristic, complemented
10#10625158C2212yes—
11#10625158C2211yescharacteristic, complemented
12#10625155C2211yescharacteristic
13C2×Q16×C23C2212yescomplemented
14C2×SD16×C23C2212yes—
15C23×C4⋊Q8C2211yescharacteristic, complemented
16C23×#124C2211yescharacteristic
17#10625113C2212yes—
18#10625113C2212yes—
19#10625113C2212yescomplemented
20#10625103C2212yes—
21#10625090—22no—
22#10625089—22no—
23#10625089—22no—
24Q16×D23—22no—
25#10625087—22no—
26#10625086—22no—
27#10625085—22no—
28SD16×D23—22no—
29#10625075C2212yes—
30#10625072C2212yes—
31#10625072C2212yescomplemented
32C23×#97C2211yescharacteristic, complemented
33#10625018C2212yescomplemented
34#10625018C2211yescharacteristic, complemented
35#10625015C2211yescharacteristic
36#10625001C2212yescomplemented
37#10624987C2212yes—
38#10624987C2212yescomplemented
39C2×Q8×C23C2311yescharacteristic
40C2×Q8×C23C2312yes—
41C2×D4×C23C2311yescharacteristic
42C2×C22⋊D23—41no—
43#67292—22no—
44#67292—22no—
45#67292—22no—
46Q8×D23—22no—
47Q8×D23—22no—
48Q8×D23—22no—
49#67290—22no—
50D4×D23—22no—
51#67288—42no—
52#67288—41no—
53#67288C2312yes—
54#67288C2312yes—
55Q16×C23—22no—
56Q16×C23—22no—
57SD16×C23—22no—
58SD16×C23—22no—
59C2×C8×C23C2312yes—
60C4⋊C4×C23—41no—
61C22⋊C4×C23—41no—
62C42×C23C2311yescharacteristic
63#67275—22no—
64#67275—22no—
65#67275—22no—
66#67274—22no—
67#67274—22no—
68#67274—22no—
69#67273—22no—
70#67272—22no—
71#67267C2312yes—
72#67267C2312yes—
73Dic92D412yes—
74D184D412yes—
75#67263D412yes—
76#67263D412yes—
77#67262—22no—
78#67262—22no—
79C8×D23—22no—
80C8×D23—22no—
81C23×C23—21no—
82C22×D23—41no—
83Q8×C23—22no—
84Q8×C23—22no—
85Q8×C23—22no—
86D4×C23—22no—
87C2×C4×C23—21no—
88C2×C4×C23—21no—
89C2×C4×C23—22no—
90C2×C4×C23C2411yescharacteristic
91C22⋊D23—22no—
92C22⋊D23—22no—
93C22⋊D23—42no—
94C2×Dic23—41no—
95D92—41no—
96D92—42no—
97D92C2×D412yes—
98D92C2×D412yes—
99C4×D23—22no—
100C4×D23—22no—
101C4×D23—42no—
102C4×D23—42no—
103C4×D23—42no—
104Dic46—41no—
105Dic46—42no—
106Dic46C2×D412yes—
107Dic46C2×D412yes—
108C8×C23C2×D412yes—
109C8×C23C2×D412yes—
110C23⋊C8—22no—
111C23⋊C8—22no—
112#3289—231nomaximal, Sylow
113C22×C23—41no—
114C22×C23—81no—
115C22×C23H(5,𝔽2)11yescharacteristic
116C2×D23—22no—
117C2×D23—22no—
118C2×D23—161no—
119C4×C23—41no—
120C4×C23—41no—
121C4×C23—42no—
122C4×C23C22×D412yes—
123Dic23—22no—
124Dic23—22no—
125#578—232no—
126#577—232no—
127#497D2311yescharacteristic, complemented
128#473—232no—
129#471—232no—
130#456—232no—
131#455—231no—
132#454—231no—
133#444—232no—
134C2×C23—21no—
135C2×C23—81no—
136C2×C23D4211yescharacteristic
137D23—42no—
138D23—42no—
1392−1+4—232no—
1402−1+4—231no—
141H(5,𝔽2)—231no—
142#137—232no—
143#137—232no—
144#137—232no—
145#137—462no—
146#137—462no—
147#137—462no—
148AGL(1,ℤ/8)—232no—
149AGL(1,ℤ/8)—462no—
150#135—232no—
151#135—462no—
152#135—462no—
153C2×Q16—462no—
154C2×Q16C2×D2312yescomplemented
155C2×SD16—462no—
156C2×SD16C2×D2312yes—
157#131—232no—
158#131—232no—
159C4⋊Q8C2×D2311yescharacteristic, complemented
160#124C2×D2311yescharacteristic
161#108—232no—
162#104—232no—
163#104—232no—
164#101—231no—
165#101—232no—
166#100—231no—
167#97C2×D2311yescharacteristic, complemented
168C23#328911yescharacteristic, complemented, Sylow
169#41—232no—
170#41—232no—
171#41—462no—
172#41—462no—
173#41—462no—
174#41—462no—
175#41—921no—
176#41—922no—
177C2×Q8—462no—
178C2×Q8—462no—
179C2×Q8—462no—
180C2×Q8C22×D2311yescharacteristic
181C2×Q8C22×D2312yes—
182C2×D4—462no—
183C2×D4—921no—
184C2×D4C22×D2311yescharacteristic
185Q16—22no—
186Q16—22no—
187Q16—232no—
188Q16—462no—
189Q16—462no—
190Q16—462no—
191SD16—22no—
192SD16—22no—
193SD16—232no—
194SD16—232no—
195SD16—462no—
196SD16—462no—
197SD16—462no—
198SD16—462no—
199D8—232no—
200D8—462no—
201M16—232no—
202M16—232no—
203M16—462no—
204M16—462no—
205C2×C8—462no—
206C2×C8—462no—
207C2×C8C22×D2312yes—
208C4⋊C4—41no—
209C22⋊C4—41no—
210C42C22×D2311yescharacteristic
211C23—21no—
212C23—921no—
213Q8—22no—
214Q8—22no—
215Q8—22no—
216Q8—232no—
217Q8—232no—
218Q8—922no—
219Q8—921no—
220D4—22no—
221D4—232no—
222D4—232no—
223D4—462no—
224D4—462no—
225D4—921no—
226D4—922no—
227D4—922no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—462no—
232C2×C4—462no—
233C2×C4—922no—
234C2×C4—922no—
235C2×C4—922no—
236C2×C4—921no—
237C2×C4C23×D2311yescharacteristic
238C8—462no—
239C8—462no—
240C8D4×D2312yes—
241C8D4×D2312yes—
242C22—41no—
243C22—81no—
244C22—462no—
245C22—462no—
246C22—3681no—
247C22#1062515511yescharacteristic
248C4—41no—
249C4—41no—
250C4—42no—
251C4—462no—
252C4—462no—
253C4C2×D4×D2312yes—
254C2—21no—
255C2—81no—
256C2—922no—
257C2—922no—
258C2#1309305211yescharacteristic
subgroupG/H
centerC2#13093052
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#497C2
socleC2×C23D42
hypercenter#497D23
hypocenterC23#3289
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #497

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13093230C2semidirect
2. #13093223C2semidirect
3. #13092689C2semidirect
4. #13092677C2semidirect
5. #13092599C2semidirect
6. #13092594C2semidirect
7. #13092589C2semidirect
8. #13092540C2semidirect
9. C23×#497C2semidirect
11. #10625158C22semidirect
13. C2×Q16×C23C22semidirect
15. C23×C4⋊Q8C22semidirect
19. #10625113C22semidirect
31. #10625072C22semidirect
32. C23×#97C22semidirect
33. #10625018C22semidirect
34. #10625018C22semidirect
36. #10625001C22semidirect
38. #10624987C22semidirect
127. #497D23semidirect
154. C2×Q16C2×D23semidirect
159. C4⋊Q8C2×D23semidirect
167. #97C2×D23semidirect
168. C23#3289semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130932302
#130932232
#130926892
#130926772
#130925992
#130925942
#130925892
#130925402
C23×#4972
#328923